2 traffic theory

Tele-traffic Theory

Tele-traffic TheoryTraffic engineering provides the basis for the analysis and design of telecommunication networks. It is not only the switching elements but also many other common shared sub systems in a telecommunication network that contribute to the blocking of a subscriber call. In a telephone network, these include digit receivers, inter-stage switching links, call processors and trunks between exchanges. The load or the traffic pattern on the network varies during the day with heavy traffic at certain times and low traffic at other times. The task of designing cost effective networks that provide the required quality of service under varied traffic conditions demands a formal scientific basis. Such a basis is provided by traffic engineering or teletraffic theory. Traffic engineering analysis enables one to determine the ability of a telecommunication network to carry a given traffic at a particular loss probability. It provides a means to determine the quantum of common equipments required to provide a particular level of service for a given traffic pattern and volume.

Network Traffic Load and Parameters

The traffic load on a typical working day during the 24 hours is shown in Fig.

Network Traffic Load and ParametersThe originating call amplitudes are relative and the actual values depend on the area where the statistics is collected. There is a little use of the network during 0 and 6 hours when most of the population is asleep. There is a large peak around mid-noon and mid-afternoon signifying busy office activities. The afternoon peak is, however, slightly smaller. The load is low during the lunch-hour period, i.e. 12.00-14.00 hours. The period 17.00-18.00 hours is characterized by low traffic signifying that the people are on the move from offices to their residences. The peak of domestic calls occurs after 18.00 hours when persons reach home and reduced tariff applies.The period during which the reduced tariff applies has been changed to begin later than 18.00 hours and one may expect the domestic call patterns also to change accordingly. During holidays and festival days the traffic pattern is different from that shown in Fig. Generally, there is a peak of calls around 10.00 hours just before people leave their homes on outings and another peak occurs again in the evening.


In a day, the 60-minute interval in which the traffic is the highest is called the busy hour (BH). The busy hour may vary from exchange to exchange depending on the location and the community interest of the subscribers. The busy hour may also show seasonal, weekly and in some places even daily variations. There are also unpredictable peaks caused by stock market or money market activity, weather, natural disaster, international events, sporting events etc. To take into account such fluctuations while designing switching networks, three types of busy hours are defined by CCITT in its recommendations E.600:

Busy Hour: Continuous 1-hour period lying wholly in the time interval concerned, for which the traffic volume or the number of call attempts is greatest.Peak Busy Hour: The busy hour each day; it usually varies from day to day, or over a number of days.Time Consistent Busy Hour: The 1-hour period starting at the same time each day for which the average traffic volume or the number of all attempts is greatest over the days under consideration.


Not all call attempts materialize into actual conversations for a variety of reasons such as called line busy, no answer from the called line, and blocking in the trunk groups or the switching centers. A call attempt is said to be successful or completed if the called party answers. Call completion rate (CCR) is defined as the ratio of the number of successful calls to the number of call attempts. The number of call attempts in the busy hour is called busy hour call attempts (BHCA), which is an important parameter in deciding the processing capacity of a common control or a stored program control system of an exchange. The CCR parameter is used in dimensioning the network capacity. Networks are usually designed to provide an overall CCR of over 0.70. A CCR value of 0.75 is considered excellent and attempts to further improve the value is generally not cost effective. A related parameter that is often used in traffic engineering calculations is the busy hour calling rate which is defined as the average number of calls originated by a subscriber during the busy hour.

EXAMPLE

An exchange serves 2000 subscribers. If the average BHCA is 10,000 and the CCR is 60%, calculate the busy hour calling rate.

SolutionAverage busy hour calls = BHCA X CCR

= 10,000 X 0.6 = 6000 calls

Busy hour calling rateAverage busy hour calls

Total number of subscribers6000 32000


The busy hour calling rate is useful in sizing the exchange to handle the peak traffic. In a rural exchange, the busy hour calling rate may be as low as 0.2, whereas in a business city it may be as high as three or more. Another useful information is to know how much of the day's total traffic is carried during the busy hour. This is measured in terms of day-to-busy hour traffic ratio which is the ratio of busy hour calling rate to the average calling rate for the day. Typically, this ratio may be over 20 for a city business area and around six or seven for a rural area.


The traffic load on a given network may be on the local switching unit, interoffice trunk lines or other common subsystems. The traffic on the network may be measured in terms of the occupancy of the servers in the network. Such a measure is called the traffic intensity which is defined as

0Period for which a server is occupied

Total period of observationA


Generally, the period of observation is taken as one hour. A0 is dimensionless. It is called erlang (E) to honor the Danish telephone engineer A.K. Erlang, who did pioneering work in traffic engineering. His paper on traffic theory published in 1909 is now regarded as a classic. A server is said to have 1 erlang of traffic if it is occupied for the entire period of observation. Traffic intensity may also be specified over a number of servers.

EXAMPLE

In a group of 10 servers, each is occupied for 30 minutes in an observation interval of two hours. Calculate the traffic carried by the group.

SolutionTraffic carried per server

Total traffic carried by the group = 10 x 0.25 E = 2.5 E

Occupied durationTotal duration

30 0.25120

E

EXAMPLE

A group of 20 servers carry a traffic of 10 erlangs. If the average duration of a call is three minutes, calculate the number of calls put through by a single server and the group as a whole in a one-hour period.

SolutionTraffic per server = 10/20 = 0.5 E

i.e. a server is busy for 30 minutes in one hour.Number of calls put through by one server = 30/3 = 10 callsTotal number of calls put through by the group = 10 X 20 = 200 calls


Traffic intensity is also measured in another way. This measure is known as centum call second (CCS) which represents a call-time product. One CCS may mean one call for 100 seconds duration or 100 calls for one second duration each or any other combination. CCS as a measure of traffic intensity is valid only in telephone circuits. For the present day networks which support voice, data and many other services, erlang is a better measure to use for representing the traffic intensity. Sometimes, call seconds (CS) and call minutes (CM) are also used as a measure of traffic intensity. We may note that

1 E = 36 CCS = 3600 CS = 60 CM

EXAMPLE

A subscriber makes three phone calls of three minutes, four minutes and two minutes duration in a one-hour period. Calculate the subscriber traffic in erlangs, CCS and CM.

Solution

3 4 2 0.1560

(3 4 2) 60 540 5.4100 100

3 4 2 9

Busy periodSubscriber traffic inerlangs ETotal period

Traffic inCCS CCS

Traffic inCS CM


Whenever we use the terminology "subscriber traffic" or "trunk traffic", we mean the traffic intensity contributed by a subscriber or the traffic intensity on a trunk. As mentioned above, traffic intensity is a call-time product. Hence two important parameters that are required to estimate the traffic intensity or the network load are

Average call arrival rate, C or Average holding time per call, th or tm

We can then express the load offered to the network in terms of these parameters asA = Cth=tm

C and th must be expressed in like time units. For example, if C () is in number of calls per minute, th (tm)must be in minutes per call.

EXAMPLE

Over a 20-minute observation interval, 40 subscribers initiate calls. Total duration of the calls is 4800 seconds. Calculate the load offered to the network by the subscribers and the average subscriber traffic.

Solution

h

Mean arrival rate C = 40/20 = 2 calls/minute4800Mean holding time t 2minutes/call

40 60Therefore,

Offered load = 2 X 2 = 4 EAverage subscriber traffic = 4/40 = 0.1 E


It is possible that the load generated by the subscribers sometimes exceeds the network capacity. There are two ways in which this overload traffic may be handled:

The overload traffic may be rejected without being serviced Calls are held in a queue until the network facilities become available.

In the first case, the calls are lost and in the second case the calls are delayed. Correspondingly, two types of systems, called

loss systems and delay systems are encountered.


Conventional automatic telephone exchanges behave like loss systems. Under overload traffic conditions a user call is blocked and is not serviced unless the user makes a retry. On the other hand, operator-oriented manual exchanges can be considered as delay systems. A good operator registers the user request and establishes connection as soon as network facilities become available without the user having to make another request. In data networks, circuit-switched networks behave as loss systems whereas store-and-forward (S&F) message or packet networks behave as delay systems. In the limit, delay systems behave as loss systems. For example, in a S&F network if the queue buffers become full, then further requests have to be rejected.


The basic performance parameters for a loss system are the grade of service and the blocking probability, and for a delay system, the service delays. Average delays, or probability of delay exceeding a certain limit, or variance of delays may be important under different circumstances. The traffic models used for studying loss systems are known as blocking or congestion models and the ones used for studying delay systems are called queuing models.

Grade of Service and Blocking Probability

In loss systems, the traffic carried by the network is generally lower than the actual traffic offered to the network by the subscribers. The overload traffic is rejected and hence is not carried by the network. The amount of traffic rejected by the network is an index of the quality of the service offered by the network. This is termed grade of service (GOS) and is defined as the ratio of lost traffic to offered traffic. Offered traffic is the product of the average number of calls generated by the users and the average holding time per call. On the other hand, the actual traffic carried by the network is called the carried traffic and is the average occupancy of the servers in the network. Accordingly, GOS is given by

0A AGOSA

A = offered traffic A0= carried traffic A — A0 = lost traffic


The smaller the value of grade of service, the better is the service. If the recommended value for GOS is 0.002 it means that two calls in every 1000 calls or one call in every 500 calls may be lost. Usually, every common subsystem in a network has an associated GOS value. The GOS of the full network is determined by the highest GOS value of the subsystems in a simplistic sense.A better estimate takes into account the connectivity of the subsystems, such as parallel units. Since the volume of traffic grows as the time passes by, the GOS value of a network deteriorates with time. In order to maintain the value within reasonable limits, initially the network is sized to have a much smaller GOS value than the recommended one so that the GOS value continues to be within limits as the network traffic grows.

The blocking probability Pb is defined as the probability that all the servers in a system are busy. When all the servers are busy, no further traffic can be carried by the system and the arriving subscriber traffic is blocked. At the first instance, it may appear that the blocking probability is the same measure as the GOS. The probability that all the servers are busy may well represent the fraction of the calls lost, which is what the GOS is all about. However, this is generally not true. For example, in a system with equal number of servers and subscribers, the GOS is zero as there is always a server available to a subscriber.


On the other hand, there is a definite probability that all the servers are busy at a given instant and hence the blocking probability is nonzero. The fundamental difference is that the GOS is a measure from the subscriber point of view whereas the blocking probability is a measure from the network or switching system point of view. GOS is arrived at by observing the number of rejected subscriber calls, whereas the blocking probability is arrived at by observing the busy servers in the switching system. GOS and Pb may have different values depending upon the traffic characterization model used. In order to distinguish between these two terms clearly, GOS is called call congestion or loss probability and the blocking probability is called time congestion.


In the case of delay systems, the traffic carried by the network is the same as the load offered to the network by the subscribers. Since the overload traffic is queued, all calls are put through the network as and when the network facilities become available. GOS as defined above is not meaningful in the case of delay systems since it has a value of zero always. The probability that a call experiences delay, termed delay probability, is a useful measure, as far as the delay systems are concerned. If the offered load or the input rate of traffic far exceeds the network capacity, then the queue lengths become very large and the calls experience undesirably long delays. Under such circumstances, the delay systems are said to be unstable as they would never be able to clear the offered load. In practice, it is possible that there are some spurts of traffic that tend to take the delay systems to the unstable region of operation. An easy way of bringing the system back to stable region of operation is to make it behave like a loss system until the queued up traffic is cleared to an acceptable limit. This technique of maintaining the stable operation is called flow control.


In more recent times, a new term called quality of service (QOS) is being used and it is considered to be more general than the GOS and includes other factors like quality of speech, error-free transmission capability etc. It is essential to recognize that there are two different important performance measures, one obtained by observing the subscriber traffic and the other by observing the network behaviour. The terms that are used synonymously in this text from the subscriber and network viewpoints are

Subscriber viewpoint:GOS = call congestion = loss probability

Network viewpoint:Blocking probability = time congestion


2 traffic theory

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